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Search: id:A164990
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| A164990 |
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Number of square involutions of n |
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+0
1
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| 1, 2, 4, 10, 22, 52, 114, 260, 564, 1256, 2698, 5908, 12588, 27224, 57620, 123432, 259816, 552400, 1157466, 2446004, 5105532, 10735352, 22334524, 46766200, 97021272, 202431152, 418935364, 871425160, 1799558584
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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F. Disanto,A. Frosini, S. Rinaldi, Square Involutions, Proceedings of Permutation Patterns, July, 13-17 2009, Florence.
T. Mansour, S. Severini, S. Grid polygons from permutations and their enumeration by the kernel method, 19-th Conference on Formal Power Series and Algebraic Combinatorics, Tianjin, China, July 2-6, 2007.
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FORMULA
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a(n)=(n+2)2^(n-3)-(n-2)C(n-3,(n-3)/2), n>1 G.f.: x(1-x)^2/(1-2x)^2-x^3/(1-2x)/sqrt(1-4x^2)
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EXAMPLE
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a(5)=22, in fact the 22 square involutions of 5 are given by all the involutions of 5, which are 26, minus 14325, 15342, 52341, 42315 which are not square.
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CROSSREFS
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Cf. A128652
Sequence in context: A033497 A075560 A078040 this_sequence A121285 A030234 A148086
Adjacent sequences: A164987 A164988 A164989 this_sequence A164991 A164992 A164993
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KEYWORD
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easy,nonn
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AUTHOR
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Simone Rinaldi (rinaldi(AT)unisi.it), Sep 04 2009
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